Dean P. Neikirk © 1999, last update May 3, 2023 1 Dept. of ECE, Univ. of Texas at Austin
Layer characterization
• need to characterize the layers produced thus far– oxides
• thickness• dielectric constant / index of refraction
– doped layers• junction depth• dopant concentrations• electrical resistance / carrier concentration
Dean P. Neikirk © 1999, last update May 3, 2023 2 Dept. of ECE, Univ. of Texas at Austin
Thickness measurements• profilometry
– mechanically measure difference in height across a “step” on the surface
• scanning “needle” traverses surface• Dektak, Tencor Alphastep
– requirements:• must have step on surface• film must be hard enough that needle does not damage it• must be calibrated using known step height
– precision / range• Alphastep specs:• profiling with 10Å (1) or 0.1% repeatability • step height metrology below 50 nm to 300 µm
from http://www.tencor.com/products/metrology/alpha-step500/AlphaStep500.pdf
Dean P. Neikirk © 1999, last update May 3, 2023 3 Dept. of ECE, Univ. of Texas at Austin
Transparent layer measurements• ellipsometry
– uses elliptically polarized light incident at an angle on the sample– state of polarization of reflected beam is dependent on
• wavelength of illumination and angle of incidence• optical constants of the “substrate”• optical constants of “covering layer”• thickness of “covering layer”
– precision / range• can measure steps of down to somewhat less than 10 nm• periodicity creates ambiguity for thicknesses over several hundred nm
http://www.afep.cornell.edu/epl/index.html
Dean P. Neikirk © 1999, last update May 3, 2023 4 Dept. of ECE, Univ. of Texas at Austin
Transparent layer measurements
• spectroscopic reflectance– measure wavelength dependence of reflectivity
Filmetrics System (figures from http://www.filmetrics.com/technology.html)
Dean P. Neikirk © 1999, last update May 3, 2023 5 Dept. of ECE, Univ. of Texas at Austin
silicon
Junction depth measurements
• non-destructive techniques– film thickness gauge
• use refractive index dependence on doping to do ellipsometry– weight gain method for epitaxial films
• junction exposing techniques
stain
optical flat
monochromaticillumination
side view
dark bands stain
top view
– interferometry used to measure gap
destructive interference
– junction lapping– chemical stain used to “electroplate” one side of junction
• when exposed to light p-n junction produces current that can drive chemical reaction on one side or other
Dean P. Neikirk © 1999, last update May 3, 2023 6 Dept. of ECE, Univ. of Texas at Austin
Junction groove technique
• grooving tool used to expose p-n junction
– stain used to delineate junction
• “electroplating” reaction used to coat either p or n side
– measure lateral distances W1, W2
RWW
WRWRx j
222
222
22
1
212
222
p-type
n-typeR R
stain
2W22
d2 xj
W1
d1
W2
W1
Dean P. Neikirk © 1999, last update May 3, 2023 7 Dept. of ECE, Univ. of Texas at Austin
Sheet resistance• consider a block of uniform conducting material
l
t
wlRt w
• Rs is the “sheet resistance” of the material• for a uniformly doped piece of semiconductor
• if the width and length are the same (i.e., it’s a “square”)
Sl wRt w t
1
orq n p
SR t or
1orS
n pq R t
Dean P. Neikirk © 1999, last update May 3, 2023 8 Dept. of ECE, Univ. of Texas at Austin
Sheet resistance measurements
• problem: contact resistance can be VERY large– use “four point”
measurement• inject current through one
pair of contacts, measure voltage across another pair
– what is relation between I, V and resistance?
V
I
a
d
t
s s s
Dean P. Neikirk © 1999, last update May 3, 2023 9 Dept. of ECE, Univ. of Texas at Austin
Sheet R from 4-point probe
• assume 2-d problem– geometry of current flow in “thin sheet”
E
J sheetsheet
I sheet2r ˆ r
total current I
perimeter 2πrcurrent density I / 2πr
• electric field/ current density relationship (Ohm’s Law!)– for a single “source” have
– but in our four point geometry have two sources: one in, and one out!
Dean P. Neikirk © 1999, last update May 3, 2023 10 Dept. of ECE, Univ. of Texas at Austin
• probe geometry produces “dipole” distribution
4-point probe
xs
IxIJE sheetsheetxx 322
s
s
s
ssheet
s
s sheet
s
s x
xsxI
dxxs
IxIdxEV
22
22
3lnln2
322
V sheetI
22 ln 2
s 2s 3s0 x
+ -
current flow and electric field lines
• along x axis is simple:
• to get voltage integrate along field line
Dean P. Neikirk © 1999, last update May 3, 2023 11 Dept. of ECE, Univ. of Texas at Austin
Final result for sheet R
• the relation between the voltage measured across the middle two probes and the current injected through the outer two probes is
sheet RS
ln 2 VI 4.54
VI
A’ B’ C’ D’
conformal map
I
I
B
C D
AVBC RS
ln 2
VBCIAD
• other probe geometries– for any bounded surface with current injected at one point on the
perimeter and removed at another, the measurement of the voltage difference between any other two points on the perimeter is sufficient to determine the sheet resistance
• Van der Pauw geometry: conducting square
Dean P. Neikirk © 1999, last update May 3, 2023 12 Dept. of ECE, Univ. of Texas at Austin
Relation between doping profile and resistance
• geometrically
1
01
jxcarriersnet
BS dxNxNNqR
xN(x1)
N(x2)
N(x3)
N(x)
x
(x)
x
– Rs ~ parallel sum of R’s from each layer• R(x) = 1 / [q • (N) • (net carriers) • x]
– resistivity & mobility are functions of ionized impurity concentration
Dean P. Neikirk © 1999, last update May 3, 2023 13 Dept. of ECE, Univ. of Texas at Austin
Mobility and resistivity for Si
1x10-5
1x10-4
1x10-3
1x10-2
1x10-1
1x100
1x101
1x102
1x103
1x10141x10151x10161x10171x10181x10191x10201x1021
resi
stiv
ity (o
hm-c
m)
impurity concentration (#/cm3)
Na (#/cm3)
Nd (#/cm3)
0200400600800
100012001400
1x1014 1x1015 1x1016 1x1017 1x1018 1x1019 1x1020
Mob
ility
(cm
2/V-
sec)
Concentration( cm-3)
electronsholes
pornqporn
11
for silicon near room temp:
91.0
17103.11
92136092
DDelectron
NN
76.0
16103.61
7.474957.47
AAhole
NN
Dean P. Neikirk © 1999, last update May 3, 2023 14 Dept. of ECE, Univ. of Texas at Austin
Irvin Curves for Si
• note that the average resistivity is given by:
1
1 1
thickness
surface
dxthickness
nnq BD NNn
Sj
x
BDj
Rx
S
dxNNqx
R
j
1
0
1
1 1
• what can we say about the value of average resistivity??
1x
0BD
jSj
j
dxNNxqRx
Dean P. Neikirk © 1999, last update May 3, 2023 15 Dept. of ECE, Univ. of Texas at Austin
Irvin Curves for Si
• note that if you specify NS, NB, xj, and the shape you have fully specified the exact doping profile!
2
, exp2
oQ xN x tDt Dt
NS
2
2exp
tDx
NN jSB
BS
j
SB
j
NNx
NNx
tDlnln
222
2
BSjS NNx
xNxNln
exp 2
2
– example: gaussian profile:
– at the junction:
1x
0B
BS2
j
2
SS
j
dxNNNlnx
xexpNqR
• can now do the sheet resistance integral since everything is known:
Dean P. Neikirk © 1999, last update May 3, 2023 16 Dept. of ECE, Univ. of Texas at Austin
Irvin Curves for Si
• calculation process– pick shape shape
surf
ace
conc
. NS
xj•Rs
• calculate sheet resistance RS
• find average resistivity = xj•Rs
• graph
– repeat for new value of NB2
NB
– pick NB, xj
• specify NS
• loopNB2
Dean P. Neikirk © 1999, last update May 3, 2023 17 Dept. of ECE, Univ. of Texas at Austin
1x1015
1x1016
1x1017
1x1018
1x1019
1x1020
1x1021
1x100 1x101 1x102 1x103 1x104 1x105
Surf
ace
Con
cent
ratio
n (c
m-3
)
Rs xj (Ohm-micron)
Rs Xj Nb=1e17
Rs Xj Nb=1e16
Rs Xj Nb=1e15
Rs Xj Nb=1e14
n-typeGaussian
NB = 1017
NB = 1016
NB = 1015
NB = 1014
Irvin Curves for Si
carrier: electronsshape: gaussian
Dean P. Neikirk © 1999, last update May 3, 2023 18 Dept. of ECE, Univ. of Texas at Austin
Irvin Curves for Si
carrier: electronsshape: erfc
1x1015
1x1016
1x1017
1x1018
1x1019
1x1020
1x1021
1x100 1x101 1x102 1x103 1x104 1x105
Surf
ace
Con
cent
ratio
n (c
m-3
)
Rs xj (Ohm-micron)
Rsxj (Nb = 1e17)
Rsxj (Nb = 1e16)
Rsxj (Nb = 1e15)
Rsxj (Nb = 1e14)
n-type Erfc
NB = 1017
NB = 1016
NB = 1015
NB = 1014
Dean P. Neikirk © 1999, last update May 3, 2023 19 Dept. of ECE, Univ. of Texas at Austin
Irvin Curves for Si
carrier: holesshape: gaussian
1x1015
1x1016
1x1017
1x1018
1x1019
1x1020
1x1021
1x101 1x102 1x103 1x104 1x105 1x106
Surf
ace
Con
cent
ratio
n (c
m-3
)
Rs xj (Ohm-micron)
Rsxj (Nb = 1e17)
Rsxj (Nb = 1e16)
Rsxj (Nb = 1e15)
Rsxj (Nb = 1e14)
p-typeGaussian
NB = 1017
NB = 1016
NB = 1015
NB = 1014
Dean P. Neikirk © 1999, last update May 3, 2023 20 Dept. of ECE, Univ. of Texas at Austin
Irvin Curves for Si
carrier: holesshape: erfc
1x1016
1x1017
1x1018
1x1019
1x1020
1x1021
1x101 1x102 1x103 1x104 1x105
Surf
ace
Con
cent
ratio
n (c
m-3
)
Rs xj (Ohm-micron)
Rsxj (Nb = 1e17)
Rsxj (Nb = 1e16)
Rsxj (Nb = 1e15)
Rsxj (Nb = 1e14)
p-type Erfc
NB = 1017
NB = 1016
NB = 1015
NB = 1014
Dean P. Neikirk © 1999, last update May 3, 2023 21 Dept. of ECE, Univ. of Texas at Austin
1x1015
1x1016
1x1017
1x1018
1x1019
1x1020
1x1021
1x100 1x101 1x102 1x103 1x104 1x105
Surf
ace
Con
cent
ratio
n (c
m-3
)
Rs xj (Ohm-micron)
Rs Xj Nb=1e17
Rs Xj Nb=1e16
Rs Xj Nb=1e15
Rs Xj Nb=1e14
n-typeGaussian
NB = 1017
NB = 1016
NB = 1015
NB = 1014
Example: need to know three of: NS, NB, xj, & RS
• n-type dopant, limited source (gaussian), NB = 1016 cm-3
Ns = 4x1018
Rs • xj ~ 2.2 x 102 (ohm-micron) for Ns = 4x1018 & NB = 1016 cm-3
NB = 1016 cm-3
Dean P. Neikirk © 1999, last update May 3, 2023 22 Dept. of ECE, Univ. of Texas at Austin
x
y
z
Hall measurements for carrier concentration
• example geometry, electrons as carriers
BvEqF
electronsholes
:
:
yBvq
yBvq
zxBvqBvqF
zx
zx
zx
electronlorentz
ˆ
ˆ
ˆˆ
xareaIj ˆ
xEE x ˆ
zBB z ˆ
xvv x ˆeln
Florentze-
• if apply magnetic field to drifting carriers a Lorentz force is generated
– note Lorentz force is proportional to velocity, direction depends on carrier type (sign of “q”)
Dean P. Neikirk © 1999, last update May 3, 2023 23 Dept. of ECE, Univ. of Texas at Austin
x
yz
xareaIj ˆ
xEE x ˆ
zBB z ˆ
xvv x ˆeln
Florentze-• side view again
Lorentz forces
xz
y
F lorentzq velectronB qvx Bz ˆ y
veln B
v x B
|qvxBz|
electron trajectories
current in current out
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
EopposedFeln opposed
xz
y
Fopposed F lorentz q vxBz ˆ y
yBvqFE z
electronx
opposedelectronopposed ˆ
• top view of sample
• but since there are no contacts on the y faces of the sample no current can flow in y direction!
Dean P. Neikirk © 1999, last update May 3, 2023 24 Dept. of ECE, Univ. of Texas at Austin
• in summary, application of “transverse” magnetic field induces an electric field in the other transverse direction
Hall effect continued
zxzxy BvBvE
x
x
external
z
external
x
measured
yH j
vBj
ER
holeselectrons
x
holeselectrons
x vpornqj
::
::
pornqvpornqv
Rx
holeselectrons
xH
1
::
HRqpn
typeptheniftypenthenif 1
,,
– - electrons– + holes
• define the Hall coefficient to be
• using a simple “drift” model we have
Dean P. Neikirk © 1999, last update May 3, 2023 25 Dept. of ECE, Univ. of Texas at Austin
• for non-uniformly doped layers can still get “sheet” parameters– essentially integral averages of µ and n
Summary of Hall & Rs measurements
RH EyV t
jxI wt
Bzmeasured
VI
wBz
n or p I Bz
qVHall1w
wtl
nqwtlR
1
x
zy jx I wt
Ey Vfronttoback
t
B Bz ˆ z
I tw
• Hall measurement gives the carrier concentration– for rectangular bar, uniform doping
• resistance gives mobility • concentration product• combination of R and RH gives mobility
Dean P. Neikirk © 1999, last update May 3, 2023 26 Dept. of ECE, Univ. of Texas at Austin
Other profiling methods
• “beam” techniques– electron
• LEED (low energy electron diffraction): structure• SEM: imaging of topology• AES (Auger spectroscopy): composition (look at energy spectrum
of emitted electrons)– ion
• SIMS (secondary ion mass spectroscopy): bombard sample with ions, look at mass of “sputtered” atoms
• RBS (Rutherford back-scattering): high energy (MeV) He bombardment, look at energy spectrum of back-scattered He
• electrical– spreading resistance, layer stripping
• measure sheet R as function of removed material– capacitance-voltage measurements
• use depletion as function of applied voltage to infer carrier profiles
Dean P. Neikirk © 1999, last update May 3, 2023 27 Dept. of ECE, Univ. of Texas at Austin
SIMS• material is “sand-blasted”
– depth information from time and sputtering rate• secondary-ion yields vary with incident ion mass and energy
– standards required to calibrate SIMS measurements• good for measurement of “low” concentrations of impurities
element primary ion detected ion detection limit
B O2+ 11B+ 1015 /cm3
P Cs+ 31P- 1016 /cm3
As Cs+ 75As- 1016 /cm3
Na O2+ 23Na+ 1014 /cm3
Fe O2+ 56Fe+ 1017 /cm3
Cu O2+ 63Cu+ 1016 /cm3
Al O2+ 27Al+ 1015 /cm3
adapted from Sze, 2nd ed., p. 542
Dean P. Neikirk © 1999, last update May 3, 2023 28 Dept. of ECE, Univ. of Texas at Austin
– reverse bias produces depletion layer, width function of doping profile and applied bias
– measure capacitance
C-V profiling
• consider p-n junction or Schottky contact
Cunitarea dQdV
sxd
ND xn C3
sqdCdV
1 ND xn
NA xp
np
0-xp xn
xd
ND xn C3
sqdCdV
– solve Poisson’s eq. for applied voltage to get (for p-n junction, assumes n = ND, p = NA):
– for p+-n (“one-sided”) junction simplifies to
• can only profile on lightly-doped side of junction
Dean P. Neikirk © 1999, last update May 3, 2023 29 Dept. of ECE, Univ. of Texas at Austin
“Layer stripping” / spreading resistance techniques
• geometrically
jxcarriersnet
BS dxNxNNqR0
1
1
xN(x1)
N(x2)
N(x3)
1/RS
xetch
RS(x)
xetch
– sequentially remove “surface” layer, then measure RS
– slope of 1/Rs curve gives N product
xxRxRxNxNxq etchSetchSBetchetch 11
x
xRxxRq
NxNx etchSetchSBetchetch
111
(x)N(x)
xetch
xxR
qNxNx etchSBetchetch
11
Dean P. Neikirk © 1999, last update May 3, 2023 30 Dept. of ECE, Univ. of Texas at Austin
Deposited thin films
• need to be able to add materials “on top” of silicon– both conductors and insulators
• deposition methods– physical vapor deposition (PVD)
• thermal evaporation• sputtering
– chemical vapor deposition (CVD)• general requirements
– good electrical characteristics– free from pin-holes, cracks– low stress– good adhesion– chemical compatibility
• with both layer “below” and “above”• at room temperature and under deposition conditions